MTH 314 Midterm: MTH314 - W2015 (Practice) Midterm
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Read all instructions before starting: calculators are not allowed, you are allowed one 8. 5 11 formula sheet (two-sided). The information on the sheet must be hand-written, with your own hand-writing: marks (out of) are shown in brackets, answer all questions in this booklet. 1 (1) (a) let p, q, and r be three statements. 2 (2) prove that the following argument form is valid: (1) (2) (3) r ( q s) ( r q) (s (u v)) (q (p p)) (s u) V v by using standard argument forms (modus ponens, modus tollens, etc. ) and logical equivalences. Be sure to justify each step, making clear which of the standard valid forms or logical equivalences you have used. You do not need to provide the names. 3 (3) prove the following statements are true: (a) X r y r such that (xy = 0 xy = 1) (b) Y q such that x r+, x > y2.
